Proper Room Acoustics/Designs

Maybe you should consider consulting Michael Green from Michael Green Audio. He tunes studios and concert halls. Getting lowest lows right is tough. He has a strong reputation in the pro-audio world. Your room as it is does seem to be messed up.

The room within a room seems it might be excessive for domestic systems. That may be more justified for recording/monitoring room designs.

A less expensive option might be utilizing 2x4 studs on 2x6 sill plates. Then stagger the studs so every other one contacts an opposite wall (while maintaining 16" spacing).

Not sure I agree with the double drywall either. Yes that may "tighten" the wall and ceiling surfaces but will it be too "dry" sounding?

Lastly, from Jim Smith's book, he recommends installing 2x4s on their side on top of a concrete slab, then overlaying wood floor on that.

A certain amount of flex can support a constructive balance in a room.

Yeah, since bass seems to be your biggest issue I'd have concerns over the proposed design. The double drywall will do little or nothing to absorb long bass waves, which means they will continue to be reflected back into your room. Secondly, since the bass diffusers are located behind the double drywall I don't see how they could solve a problem that would already have occurred inside your room. Seems like that design would possibly help reduce transmitting bass outside (or outside sound getting into) your room but not do much for the sound inside your room.

I must have not done a very good job of describing the room. There won't be any drywall-at all. 2 x 12's on all 6 walls, floor, etc. Sound diffusers and bass traps will be incorporated in the walls where ever is needed. The bass traps are like Hemholtz devices, with the diffusers being vertical/horizontal slats. The outer walls will have material over them. Just look up Dennis Foley, to see his designs.